The simplex geometry of graphs

Review (2019)

Authors

Karel Devriendt University of Oxford, Student
P.F.A. Van Mieghem Network Architectures and Services - EEMCS
Research Group
Network Architectures and Services (EEMCS) (TU Delft)
Copyright: © 2019 Karel Devriendt, P.F.A. Van Mieghem
DOI: https://doi.org/10.1093/comnet/cny036
Laplacian matrix Graph embedding Geometry of graphs Simplex geometry
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Published Date

2019-8

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Quantum & Computer Engineering

Research Group

Network Architectures and Services

Abstract

Graphs are a central object of study in various scientific fields, such as discrete mathematics, theoretical computer science and network science. These graphs are typically studied using combinatorial, algebraic or probabilistic methods, each of which highlights the properties of graphs in a uniqueway. Here, we discuss a novel approach to study graphs: the simplex geometry (a simplex is a generalized triangle). This perspective, proposed by Miroslav Fiedler, introduces techniques from (simplex) geometry into the field of graph theory and conversely, via an exact correspondence. We introduce this graph-simplex correspondence, identify a number of basic connections between graph characteristics and simplex properties, and suggest some applications as example.